Newform orbit 124.4.g.a

• Label: 124.4.g.a
• Level: $124$
• Weight: $4$
• Character orbit: 124.g
• Analytic conductor: $7.316$
• Analytic rank: $0$
• Dimension: $92$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	124.g (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.31623684071\)
Analytic rank:	\(0\)
Dimension:	\(92\)
Relative dimension:	\(46\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 92 q - 4 q^{2} - 16 q^{4} - 2 q^{5} - 6 q^{6} + 32 q^{8} - 380 q^{9}+O(q^{10}) \)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
99.1	−2.82559	−	0.126693i	−4.91798	−	8.51819i	7.96790	+	0.715964i	−6.27867	+	10.8750i	12.8170	+	24.6920i	15.4782	−	8.93635i	−22.4233	−	3.03249i	−34.8730	+	60.4018i	19.1187	−	29.9327i
99.2	−2.82559	+	0.126693i	4.91798	+	8.51819i	7.96790	−	0.715964i	−6.27867	+	10.8750i	−14.9754	−	23.4458i	−15.4782	+	8.93635i	−22.4233	+	3.03249i	−34.8730	+	60.4018i	16.3631	−	31.5237i
99.3	−2.79938	−	0.404321i	−1.11241	−	1.92675i	7.67305	+	2.26370i	−0.442075	+	0.765697i	2.33503	+	5.84347i	−10.6019	+	6.12103i	−20.5645	−	9.43932i	11.0251	−	19.0960i	1.54712	−	1.96474i
99.4	−2.79938	+	0.404321i	1.11241	+	1.92675i	7.67305	−	2.26370i	−0.442075	+	0.765697i	−3.89308	−	4.94393i	10.6019	−	6.12103i	−20.5645	+	9.43932i	11.0251	−	19.0960i	0.927949	−	2.32222i
99.5	−2.55149	−	1.22061i	2.55065	+	4.41786i	5.02024	+	6.22874i	9.17529	−	15.8921i	−1.11551	−	14.3855i	−6.94044	+	4.00706i	−5.20629	−	22.0203i	0.488345	−	0.845838i	−42.8086	+	29.3491i
99.6	−2.55149	+	1.22061i	−2.55065	−	4.41786i	5.02024	−	6.22874i	9.17529	−	15.8921i	11.9004	+	8.15880i	6.94044	−	4.00706i	−5.20629	+	22.0203i	0.488345	−	0.845838i	−4.01275	+	51.7479i
99.7	−2.37901	−	1.52980i	3.19400	+	5.53217i	3.31940	+	7.27884i	−4.09410	+	7.09120i	0.864566	−	18.0473i	29.0956	−	16.7983i	3.23830	−	22.3945i	−6.90326	+	11.9568i	20.5881	−	10.6069i
99.8	−2.37901	+	1.52980i	−3.19400	−	5.53217i	3.31940	−	7.27884i	−4.09410	+	7.09120i	16.0617	+	8.27491i	−29.0956	+	16.7983i	3.23830	+	22.3945i	−6.90326	+	11.9568i	−1.10821	−	23.1332i
99.9	−2.31093	−	1.63082i	−3.25999	−	5.64646i	2.68083	+	7.53745i	5.80855	−	10.0607i	−1.67477	+	18.3651i	22.4498	−	12.9614i	6.09702	−	21.7905i	−7.75503	+	13.4321i	−29.8304	+	13.7769i
99.10	−2.31093	+	1.63082i	3.25999	+	5.64646i	2.68083	−	7.53745i	5.80855	−	10.0607i	−16.7420	−	7.73214i	−22.4498	+	12.9614i	6.09702	+	21.7905i	−7.75503	+	13.4321i	2.98405	+	32.7223i
99.11	−2.19576	−	1.78288i	−1.28634	−	2.22801i	1.64271	+	7.82953i	−10.4985	+	18.1839i	−1.14777	+	7.18554i	−0.769829	+	0.444461i	10.3521	−	20.1205i	10.1907	−	17.6507i	55.4717	−	21.2100i
99.12	−2.19576	+	1.78288i	1.28634	+	2.22801i	1.64271	−	7.82953i	−10.4985	+	18.1839i	−6.79675	−	2.59878i	0.769829	−	0.444461i	10.3521	+	20.1205i	10.1907	−	17.6507i	−9.36750	−	58.6449i
99.13	−1.93657	−	2.06148i	−2.99160	−	5.18160i	−0.499411	+	7.98440i	2.78744	−	4.82798i	−4.88834	+	16.2016i	−21.0345	+	12.1443i	17.4268	−	14.4328i	−4.39930	+	7.61981i	−15.3509	+	3.60347i
99.14	−1.93657	+	2.06148i	2.99160	+	5.18160i	−0.499411	−	7.98440i	2.78744	−	4.82798i	−16.4752	−	3.86739i	21.0345	−	12.1443i	17.4268	+	14.4328i	−4.39930	+	7.61981i	4.55474	+	15.0960i
99.15	−1.56875	−	2.35351i	3.48040	+	6.02822i	−3.07805	+	7.38414i	−1.91752	+	3.32125i	8.72764	−	17.6479i	−14.1721	+	8.18229i	22.2074	−	4.33964i	−10.7263	+	18.5785i	10.8247	−	0.697288i
99.16	−1.56875	+	2.35351i	−3.48040	−	6.02822i	−3.07805	−	7.38414i	−1.91752	+	3.32125i	19.6474	+	1.26561i	14.1721	−	8.18229i	22.2074	+	4.33964i	−10.7263	+	18.5785i	−4.80849	−	9.72313i
99.17	−0.926133	−	2.67250i	0.841228	+	1.45705i	−6.28456	+	4.95019i	−1.39353	+	2.41367i	3.11488	−	3.59761i	−4.84379	+	2.79656i	19.0497	+	12.2110i	12.0847	−	20.9313i	7.74115	+	1.48885i
99.18	−0.926133	+	2.67250i	−0.841228	−	1.45705i	−6.28456	−	4.95019i	−1.39353	+	2.41367i	4.67306	−	0.898764i	4.84379	−	2.79656i	19.0497	−	12.2110i	12.0847	−	20.9313i	−5.15995	−	5.95961i
99.19	−0.838686	−	2.70122i	−0.763877	−	1.32307i	−6.59321	+	4.53095i	4.63139	−	8.02180i	−2.93327	+	3.17305i	26.7280	−	15.4314i	17.7687	+	14.0097i	12.3330	−	21.3614i	−25.5529	−	5.78264i
99.20	−0.838686	+	2.70122i	0.763877	+	1.32307i	−6.59321	−	4.53095i	4.63139	−	8.02180i	−4.21457	+	0.953760i	−26.7280	+	15.4314i	17.7687	−	14.0097i	12.3330	−	21.3614i	17.7844	+	19.2382i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
31.e	odd	6	1	inner
124.g	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	124.4.g.a	✓	92
4.b	odd	2	1	inner	124.4.g.a	✓	92
31.e	odd	6	1	inner	124.4.g.a	✓	92
124.g	even	6	1	inner	124.4.g.a	✓	92

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
124.4.g.a	✓	92	1.a	even	1	1	trivial
124.4.g.a	✓	92	4.b	odd	2	1	inner
124.4.g.a	✓	92	31.e	odd	6	1	inner
124.4.g.a	✓	92	124.g	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(124, [\chi])\).